A fork in a blockchain is a change to the rules by which a block is recognized as valid. There are soft forks and hard forks, which affect the unity of the network in different ways.
A cryptocurrency fork is a new coin created on the basis of existing code or an algorithm with certain changes made to it. This is how altcoins based on Bitcoin and Litecoin came about.
A soft fork is a soft update of a cryptocurrency protocol that is compatible with older versions of the software, in which the network continues to operate as a single whole and is not split into separate chains.